#include "../gpl/gpl.h"

#include <set>
#ifdef _WIN32
#include <winsock.h>
#else
#include <time.h>
#endif

// source: https://stackoverflow.com/questions/5167269/clock-gettime-alternative-in-mac-os-x
#ifdef __APPLE__
#include <mach/mach_time.h>
#define ORWL_NANO (+1.0E-9)
#define ORWL_GIGA UINT64_C(1000000000)

static double   orwl_timebase  = 0.0;
static uint64_t orwl_timestart = 0;

struct timespec orwl_gettime(void) {
  // be more careful in a multithreaded environement
  if(!orwl_timestart) {
    mach_timebase_info_data_t tb = {0};
    mach_timebase_info(&tb);
    orwl_timebase = tb.numer;
    orwl_timebase /= tb.denom;
    orwl_timestart = mach_absolute_time();
  }
  struct timespec t;
  double          diff = (mach_absolute_time() - orwl_timestart) * orwl_timebase;
  t.tv_sec             = diff * ORWL_NANO;
  t.tv_nsec            = diff - (t.tv_sec * ORWL_GIGA);
  return t;
}
#endif // __APPLE__

const double WGS84_A     = 6378137.0;
const double WGS84_ECCSQ = 0.00669437999013;

// Windows lacks fminf
#ifndef fminf
#define fminf(x, y) (((x) < (y)) ? (x) : (y))
#endif

namespace camodocal {

double hypot3(double x, double y, double z) {
  return sqrt(square(x) + square(y) + square(z));
}

float hypot3f(float x, float y, float z) {
  return sqrtf(square(x) + square(y) + square(z));
}

double d2r(double deg) {
  return deg / 180.0 * M_PI;
}

float d2r(float deg) {
  return deg / 180.0f * M_PI;
}

double r2d(double rad) {
  return rad / M_PI * 180.0;
}

float r2d(float rad) {
  return rad / M_PI * 180.0f;
}

double sinc(double theta) {
  return sin(theta) / theta;
}

float colormapAutumn[128][3] =
  {
    {1.0f, 0.f, 0.f},
    {1.0f, 0.007874f, 0.f},
    {1.0f, 0.015748f, 0.f},
    {1.0f, 0.023622f, 0.f},
    {1.0f, 0.031496f, 0.f},
    {1.0f, 0.03937f, 0.f},
    {1.0f, 0.047244f, 0.f},
    {1.0f, 0.055118f, 0.f},
    {1.0f, 0.062992f, 0.f},
    {1.0f, 0.070866f, 0.f},
    {1.0f, 0.07874f, 0.f},
    {1.0f, 0.086614f, 0.f},
    {1.0f, 0.094488f, 0.f},
    {1.0f, 0.10236f, 0.f},
    {1.0f, 0.11024f, 0.f},
    {1.0f, 0.11811f, 0.f},
    {1.0f, 0.12598f, 0.f},
    {1.0f, 0.13386f, 0.f},
    {1.0f, 0.14173f, 0.f},
    {1.0f, 0.14961f, 0.f},
    {1.0f, 0.15748f, 0.f},
    {1.0f, 0.16535f, 0.f},
    {1.0f, 0.17323f, 0.f},
    {1.0f, 0.1811f, 0.f},
    {1.0f, 0.18898f, 0.f},
    {1.0f, 0.19685f, 0.f},
    {1.0f, 0.20472f, 0.f},
    {1.0f, 0.2126f, 0.f},
    {1.0f, 0.22047f, 0.f},
    {1.0f, 0.22835f, 0.f},
    {1.0f, 0.23622f, 0.f},
    {1.0f, 0.24409f, 0.f},
    {1.0f, 0.25197f, 0.f},
    {1.0f, 0.25984f, 0.f},
    {1.0f, 0.26772f, 0.f},
    {1.0f, 0.27559f, 0.f},
    {1.0f, 0.28346f, 0.f},
    {1.0f, 0.29134f, 0.f},
    {1.0f, 0.29921f, 0.f},
    {1.0f, 0.30709f, 0.f},
    {1.0f, 0.31496f, 0.f},
    {1.0f, 0.32283f, 0.f},
    {1.0f, 0.33071f, 0.f},
    {1.0f, 0.33858f, 0.f},
    {1.0f, 0.34646f, 0.f},
    {1.0f, 0.35433f, 0.f},
    {1.0f, 0.3622f, 0.f},
    {1.0f, 0.37008f, 0.f},
    {1.0f, 0.37795f, 0.f},
    {1.0f, 0.38583f, 0.f},
    {1.0f, 0.3937f, 0.f},
    {1.0f, 0.40157f, 0.f},
    {1.0f, 0.40945f, 0.f},
    {1.0f, 0.41732f, 0.f},
    {1.0f, 0.4252f, 0.f},
    {1.0f, 0.43307f, 0.f},
    {1.0f, 0.44094f, 0.f},
    {1.0f, 0.44882f, 0.f},
    {1.0f, 0.45669f, 0.f},
    {1.0f, 0.46457f, 0.f},
    {1.0f, 0.47244f, 0.f},
    {1.0f, 0.48031f, 0.f},
    {1.0f, 0.48819f, 0.f},
    {1.0f, 0.49606f, 0.f},
    {1.0f, 0.50394f, 0.f},
    {1.0f, 0.51181f, 0.f},
    {1.0f, 0.51969f, 0.f},
    {1.0f, 0.52756f, 0.f},
    {1.0f, 0.53543f, 0.f},
    {1.0f, 0.54331f, 0.f},
    {1.0f, 0.55118f, 0.f},
    {1.0f, 0.55906f, 0.f},
    {1.0f, 0.56693f, 0.f},
    {1.0f, 0.5748f, 0.f},
    {1.0f, 0.58268f, 0.f},
    {1.0f, 0.59055f, 0.f},
    {1.0f, 0.59843f, 0.f},
    {1.0f, 0.6063f, 0.f},
    {1.0f, 0.61417f, 0.f},
    {1.0f, 0.62205f, 0.f},
    {1.0f, 0.62992f, 0.f},
    {1.0f, 0.6378f, 0.f},
    {1.0f, 0.64567f, 0.f},
    {1.0f, 0.65354f, 0.f},
    {1.0f, 0.66142f, 0.f},
    {1.0f, 0.66929f, 0.f},
    {1.0f, 0.67717f, 0.f},
    {1.0f, 0.68504f, 0.f},
    {1.0f, 0.69291f, 0.f},
    {1.0f, 0.70079f, 0.f},
    {1.0f, 0.70866f, 0.f},
    {1.0f, 0.71654f, 0.f},
    {1.0f, 0.72441f, 0.f},
    {1.0f, 0.73228f, 0.f},
    {1.0f, 0.74016f, 0.f},
    {1.0f, 0.74803f, 0.f},
    {1.0f, 0.75591f, 0.f},
    {1.0f, 0.76378f, 0.f},
    {1.0f, 0.77165f, 0.f},
    {1.0f, 0.77953f, 0.f},
    {1.0f, 0.7874f, 0.f},
    {1.0f, 0.79528f, 0.f},
    {1.0f, 0.80315f, 0.f},
    {1.0f, 0.81102f, 0.f},
    {1.0f, 0.8189f, 0.f},
    {1.0f, 0.82677f, 0.f},
    {1.0f, 0.83465f, 0.f},
    {1.0f, 0.84252f, 0.f},
    {1.0f, 0.85039f, 0.f},
    {1.0f, 0.85827f, 0.f},
    {1.0f, 0.86614f, 0.f},
    {1.0f, 0.87402f, 0.f},
    {1.0f, 0.88189f, 0.f},
    {1.0f, 0.88976f, 0.f},
    {1.0f, 0.89764f, 0.f},
    {1.0f, 0.90551f, 0.f},
    {1.0f, 0.91339f, 0.f},
    {1.0f, 0.92126f, 0.f},
    {1.0f, 0.92913f, 0.f},
    {1.0f, 0.93701f, 0.f},
    {1.0f, 0.94488f, 0.f},
    {1.0f, 0.95276f, 0.f},
    {1.0f, 0.96063f, 0.f},
    {1.0f, 0.9685f, 0.f},
    {1.0f, 0.97638f, 0.f},
    {1.0f, 0.98425f, 0.f},
    {1.0f, 0.99213f, 0.f},
    {1.0f, 1.0f, 0.0f}};

float colormapJet[128][3] =
  {
    {0.0f, 0.0f, 0.53125f},
    {0.0f, 0.0f, 0.5625f},
    {0.0f, 0.0f, 0.59375f},
    {0.0f, 0.0f, 0.625f},
    {0.0f, 0.0f, 0.65625f},
    {0.0f, 0.0f, 0.6875f},
    {0.0f, 0.0f, 0.71875f},
    {0.0f, 0.0f, 0.75f},
    {0.0f, 0.0f, 0.78125f},
    {0.0f, 0.0f, 0.8125f},
    {0.0f, 0.0f, 0.84375f},
    {0.0f, 0.0f, 0.875f},
    {0.0f, 0.0f, 0.90625f},
    {0.0f, 0.0f, 0.9375f},
    {0.0f, 0.0f, 0.96875f},
    {0.0f, 0.0f, 1.0f},
    {0.0f, 0.03125f, 1.0f},
    {0.0f, 0.0625f, 1.0f},
    {0.0f, 0.09375f, 1.0f},
    {0.0f, 0.125f, 1.0f},
    {0.0f, 0.15625f, 1.0f},
    {0.0f, 0.1875f, 1.0f},
    {0.0f, 0.21875f, 1.0f},
    {0.0f, 0.25f, 1.0f},
    {0.0f, 0.28125f, 1.0f},
    {0.0f, 0.3125f, 1.0f},
    {0.0f, 0.34375f, 1.0f},
    {0.0f, 0.375f, 1.0f},
    {0.0f, 0.40625f, 1.0f},
    {0.0f, 0.4375f, 1.0f},
    {0.0f, 0.46875f, 1.0f},
    {0.0f, 0.5f, 1.0f},
    {0.0f, 0.53125f, 1.0f},
    {0.0f, 0.5625f, 1.0f},
    {0.0f, 0.59375f, 1.0f},
    {0.0f, 0.625f, 1.0f},
    {0.0f, 0.65625f, 1.0f},
    {0.0f, 0.6875f, 1.0f},
    {0.0f, 0.71875f, 1.0f},
    {0.0f, 0.75f, 1.0f},
    {0.0f, 0.78125f, 1.0f},
    {0.0f, 0.8125f, 1.0f},
    {0.0f, 0.84375f, 1.0f},
    {0.0f, 0.875f, 1.0f},
    {0.0f, 0.90625f, 1.0f},
    {0.0f, 0.9375f, 1.0f},
    {0.0f, 0.96875f, 1.0f},
    {0.0f, 1.0f, 1.0f},
    {0.03125f, 1.0f, 0.96875f},
    {0.0625f, 1.0f, 0.9375f},
    {0.09375f, 1.0f, 0.90625f},
    {0.125f, 1.0f, 0.875f},
    {0.15625f, 1.0f, 0.84375f},
    {0.1875f, 1.0f, 0.8125f},
    {0.21875f, 1.0f, 0.78125f},
    {0.25f, 1.0f, 0.75f},
    {0.28125f, 1.0f, 0.71875f},
    {0.3125f, 1.0f, 0.6875f},
    {0.34375f, 1.0f, 0.65625f},
    {0.375f, 1.0f, 0.625f},
    {0.40625f, 1.0f, 0.59375f},
    {0.4375f, 1.0f, 0.5625f},
    {0.46875f, 1.0f, 0.53125f},
    {0.5f, 1.0f, 0.5f},
    {0.53125f, 1.0f, 0.46875f},
    {0.5625f, 1.0f, 0.4375f},
    {0.59375f, 1.0f, 0.40625f},
    {0.625f, 1.0f, 0.375f},
    {0.65625f, 1.0f, 0.34375f},
    {0.6875f, 1.0f, 0.3125f},
    {0.71875f, 1.0f, 0.28125f},
    {0.75f, 1.0f, 0.25f},
    {0.78125f, 1.0f, 0.21875f},
    {0.8125f, 1.0f, 0.1875f},
    {0.84375f, 1.0f, 0.15625f},
    {0.875f, 1.0f, 0.125f},
    {0.90625f, 1.0f, 0.09375f},
    {0.9375f, 1.0f, 0.0625f},
    {0.96875f, 1.0f, 0.03125f},
    {1.0f, 1.0f, 0.0f},
    {1.0f, 0.96875f, 0.0f},
    {1.0f, 0.9375f, 0.0f},
    {1.0f, 0.90625f, 0.0f},
    {1.0f, 0.875f, 0.0f},
    {1.0f, 0.84375f, 0.0f},
    {1.0f, 0.8125f, 0.0f},
    {1.0f, 0.78125f, 0.0f},
    {1.0f, 0.75f, 0.0f},
    {1.0f, 0.71875f, 0.0f},
    {1.0f, 0.6875f, 0.0f},
    {1.0f, 0.65625f, 0.0f},
    {1.0f, 0.625f, 0.0f},
    {1.0f, 0.59375f, 0.0f},
    {1.0f, 0.5625f, 0.0f},
    {1.0f, 0.53125f, 0.0f},
    {1.0f, 0.5f, 0.0f},
    {1.0f, 0.46875f, 0.0f},
    {1.0f, 0.4375f, 0.0f},
    {1.0f, 0.40625f, 0.0f},
    {1.0f, 0.375f, 0.0f},
    {1.0f, 0.34375f, 0.0f},
    {1.0f, 0.3125f, 0.0f},
    {1.0f, 0.28125f, 0.0f},
    {1.0f, 0.25f, 0.0f},
    {1.0f, 0.21875f, 0.0f},
    {1.0f, 0.1875f, 0.0f},
    {1.0f, 0.15625f, 0.0f},
    {1.0f, 0.125f, 0.0f},
    {1.0f, 0.09375f, 0.0f},
    {1.0f, 0.0625f, 0.0f},
    {1.0f, 0.03125f, 0.0f},
    {1.0f, 0.0f, 0.0f},
    {0.96875f, 0.0f, 0.0f},
    {0.9375f, 0.0f, 0.0f},
    {0.90625f, 0.0f, 0.0f},
    {0.875f, 0.0f, 0.0f},
    {0.84375f, 0.0f, 0.0f},
    {0.8125f, 0.0f, 0.0f},
    {0.78125f, 0.0f, 0.0f},
    {0.75f, 0.0f, 0.0f},
    {0.71875f, 0.0f, 0.0f},
    {0.6875f, 0.0f, 0.0f},
    {0.65625f, 0.0f, 0.0f},
    {0.625f, 0.0f, 0.0f},
    {0.59375f, 0.0f, 0.0f},
    {0.5625f, 0.0f, 0.0f},
    {0.53125f, 0.0f, 0.0f},
    {0.5f, 0.0f, 0.0f}};

void colorDepthImage(cv::Mat& imgDepth, cv::Mat& imgColoredDepth, float minRange, float maxRange) {
  imgColoredDepth = cv::Mat::zeros(imgDepth.size(), CV_8UC3);

  for(int i = 0; i < imgColoredDepth.rows; ++i) {
    const float*   depth = imgDepth.ptr<float>(i);
    unsigned char* pixel = imgColoredDepth.ptr<unsigned char>(i);
    for(int j = 0; j < imgColoredDepth.cols; ++j) {
      if(depth[j] != 0) {
        int idx = fminf(depth[j] - minRange, maxRange - minRange) / (maxRange - minRange) * 127.0f;
        idx     = 127 - idx;

        pixel[0] = colormapJet[idx][2] * 255.0f;
        pixel[1] = colormapJet[idx][1] * 255.0f;
        pixel[2] = colormapJet[idx][0] * 255.0f;
      }

      pixel += 3;
    }
  }
}

bool colormap(const std::string& name, unsigned char idx, float& r, float& g, float& b) {
  if(name.compare("jet") == 0) {
    float* color = colormapJet[idx];

    r = color[0];
    g = color[1];
    b = color[2];

    return true;
  }
  else if(name.compare("autumn") == 0) {
    float* color = colormapAutumn[idx];

    r = color[0];
    g = color[1];
    b = color[2];

    return true;
  }

  return false;
}

std::vector<cv::Point2i> bresLine(int x0, int y0, int x1, int y1) {
  // Bresenham's line algorithm
  // Find cells intersected by line between (x0,y0) and (x1,y1)

  std::vector<cv::Point2i> cells;

  int dx = std::abs(x1 - x0);
  int dy = std::abs(y1 - y0);

  int sx = (x0 < x1) ? 1 : -1;
  int sy = (y0 < y1) ? 1 : -1;

  int err = dx - dy;

  while(1) {
    cells.push_back(cv::Point2i(x0, y0));

    if(x0 == x1 && y0 == y1) {
      break;
    }

    int e2 = 2 * err;
    if(e2 > -dy) {
      err -= dy;
      x0 += sx;
    }
    if(e2 < dx) {
      err += dx;
      y0 += sy;
    }
  }

  return cells;
}

std::vector<cv::Point2i> bresCircle(int x0, int y0, int r) {
  // Bresenham's circle algorithm
  // Find cells intersected by circle with center (x0,y0) and radius r

  std::vector<std::vector<bool>> mask(2 * r + 1);

  for(int i = 0; i < 2 * r + 1; ++i) {
    mask[i].resize(2 * r + 1);
    for(int j = 0; j < 2 * r + 1; ++j) {
      mask[i][j] = false;
    }
  }

  int f     = 1 - r;
  int ddF_x = 1;
  int ddF_y = -2 * r;
  int x     = 0;
  int y     = r;

  std::vector<cv::Point2i> line;

  line = bresLine(x0, y0 - r, x0, y0 + r);
  for(std::vector<cv::Point2i>::iterator it = line.begin(); it != line.end(); ++it) {
    mask[it->x - x0 + r][it->y - y0 + r] = true;
  }

  line = bresLine(x0 - r, y0, x0 + r, y0);
  for(std::vector<cv::Point2i>::iterator it = line.begin(); it != line.end(); ++it) {
    mask[it->x - x0 + r][it->y - y0 + r] = true;
  }

  while(x < y) {
    if(f >= 0) {
      y--;
      ddF_y += 2;
      f += ddF_y;
    }

    x++;
    ddF_x += 2;
    f += ddF_x;

    line = bresLine(x0 - x, y0 + y, x0 + x, y0 + y);
    for(std::vector<cv::Point2i>::iterator it = line.begin(); it != line.end(); ++it) {
      mask[it->x - x0 + r][it->y - y0 + r] = true;
    }

    line = bresLine(x0 - x, y0 - y, x0 + x, y0 - y);
    for(std::vector<cv::Point2i>::iterator it = line.begin(); it != line.end(); ++it) {
      mask[it->x - x0 + r][it->y - y0 + r] = true;
    }

    line = bresLine(x0 - y, y0 + x, x0 + y, y0 + x);
    for(std::vector<cv::Point2i>::iterator it = line.begin(); it != line.end(); ++it) {
      mask[it->x - x0 + r][it->y - y0 + r] = true;
    }

    line = bresLine(x0 - y, y0 - x, x0 + y, y0 - x);
    for(std::vector<cv::Point2i>::iterator it = line.begin(); it != line.end(); ++it) {
      mask[it->x - x0 + r][it->y - y0 + r] = true;
    }
  }

  std::vector<cv::Point2i> cells;
  for(int i = 0; i < 2 * r + 1; ++i) {
    for(int j = 0; j < 2 * r + 1; ++j) {
      if(mask[i][j]) {
        cells.push_back(cv::Point2i(i - r + x0, j - r + y0));
      }
    }
  }

  return cells;
}

void fitCircle(const std::vector<cv::Point2d>& points,
               double&                         centerX,
               double&                         centerY,
               double&                         radius) {
  // D. Umbach, and K. Jones, A Few Methods for Fitting Circles to Data,
  // IEEE Transactions on Instrumentation and Measurement, 2000
  // We use the modified least squares method.
  double sum_x   = 0.0;
  double sum_y   = 0.0;
  double sum_xx  = 0.0;
  double sum_xy  = 0.0;
  double sum_yy  = 0.0;
  double sum_xxx = 0.0;
  double sum_xxy = 0.0;
  double sum_xyy = 0.0;
  double sum_yyy = 0.0;

  int n = points.size();
  for(int i = 0; i < n; ++i) {
    double x = points.at(i).x;
    double y = points.at(i).y;

    sum_x += x;
    sum_y += y;
    sum_xx += x * x;
    sum_xy += x * y;
    sum_yy += y * y;
    sum_xxx += x * x * x;
    sum_xxy += x * x * y;
    sum_xyy += x * y * y;
    sum_yyy += y * y * y;
  }

  double A = n * sum_xx - square(sum_x);
  double B = n * sum_xy - sum_x * sum_y;
  double C = n * sum_yy - square(sum_y);
  double D = 0.5 * (n * sum_xyy - sum_x * sum_yy + n * sum_xxx - sum_x * sum_xx);
  double E = 0.5 * (n * sum_xxy - sum_y * sum_xx + n * sum_yyy - sum_y * sum_yy);

  centerX = (D * C - B * E) / (A * C - square(B));
  centerY = (A * E - B * D) / (A * C - square(B));

  double sum_r = 0.0;
  for(int i = 0; i < n; ++i) {
    double x = points.at(i).x;
    double y = points.at(i).y;

    sum_r += hypot(x - centerX, y - centerY);
  }

  radius = sum_r / n;
}

std::vector<cv::Point2d>
intersectCircles(double x1, double y1, double r1, double x2, double y2, double r2) {
  std::vector<cv::Point2d> ipts;

  double d = hypot(x1 - x2, y1 - y2);
  if(d > r1 + r2) {
    // circles are separate
    return ipts;
  }
  if(d < fabs(r1 - r2)) {
    // one circle is contained within the other
    return ipts;
  }

  double a = (square(r1) - square(r2) + square(d)) / (2.0 * d);
  double h = sqrt(square(r1) - square(a));

  double x3 = x1 + a * (x2 - x1) / d;
  double y3 = y1 + a * (y2 - y1) / d;

  if(h < 1e-10) {
    // two circles touch at one point
    ipts.push_back(cv::Point2d(x3, y3));
    return ipts;
  }

  ipts.push_back(cv::Point2d(x3 + h * (y2 - y1) / d,
                             y3 - h * (x2 - x1) / d));
  ipts.push_back(cv::Point2d(x3 - h * (y2 - y1) / d,
                             y3 + h * (x2 - x1) / d));
  return ipts;
}

char UTMLetterDesignator(double latitude) {
  // This routine determines the correct UTM letter designator for the given latitude
  // returns 'Z' if latitude is outside the UTM limits of 84N to 80S
  // Written by Chuck Gantz- chuck.gantz@globalstar.com
  char letterDesignator;

  if((84.0 >= latitude) && (latitude >= 72.0))
    letterDesignator = 'X';
  else if((72.0 > latitude) && (latitude >= 64.0))
    letterDesignator = 'W';
  else if((64.0 > latitude) && (latitude >= 56.0))
    letterDesignator = 'V';
  else if((56.0 > latitude) && (latitude >= 48.0))
    letterDesignator = 'U';
  else if((48.0 > latitude) && (latitude >= 40.0))
    letterDesignator = 'T';
  else if((40.0 > latitude) && (latitude >= 32.0))
    letterDesignator = 'S';
  else if((32.0 > latitude) && (latitude >= 24.0))
    letterDesignator = 'R';
  else if((24.0 > latitude) && (latitude >= 16.0))
    letterDesignator = 'Q';
  else if((16.0 > latitude) && (latitude >= 8.0))
    letterDesignator = 'P';
  else if((8.0 > latitude) && (latitude >= 0.0))
    letterDesignator = 'N';
  else if((0.0 > latitude) && (latitude >= -8.0))
    letterDesignator = 'M';
  else if((-8.0 > latitude) && (latitude >= -16.0))
    letterDesignator = 'L';
  else if((-16.0 > latitude) && (latitude >= -24.0))
    letterDesignator = 'K';
  else if((-24.0 > latitude) && (latitude >= -32.0))
    letterDesignator = 'J';
  else if((-32.0 > latitude) && (latitude >= -40.0))
    letterDesignator = 'H';
  else if((-40.0 > latitude) && (latitude >= -48.0))
    letterDesignator = 'G';
  else if((-48.0 > latitude) && (latitude >= -56.0))
    letterDesignator = 'F';
  else if((-56.0 > latitude) && (latitude >= -64.0))
    letterDesignator = 'E';
  else if((-64.0 > latitude) && (latitude >= -72.0))
    letterDesignator = 'D';
  else if((-72.0 > latitude) && (latitude >= -80.0))
    letterDesignator = 'C';
  else
    letterDesignator = 'Z'; //This is here as an error flag to show that the Latitude is outside the UTM limits

  return letterDesignator;
}

void LLtoUTM(double latitude, double longitude, double& utmNorthing, double& utmEasting, std::string& utmZone) {
  // converts lat/long to UTM coords.  Equations from USGS Bulletin 1532
  // East Longitudes are positive, West longitudes are negative.
  // North latitudes are positive, South latitudes are negative
  // Lat and Long are in decimal degrees
  // Written by Chuck Gantz- chuck.gantz@globalstar.com

  double k0 = 0.9996;

  double LongOrigin;
  double eccPrimeSquared;
  double N, T, C, A, M;

  double LatRad  = latitude * M_PI / 180.0;
  double LongRad = longitude * M_PI / 180.0;
  double LongOriginRad;

  int ZoneNumber = static_cast<int>((longitude + 180.0) / 6.0) + 1;

  if(latitude >= 56.0 && latitude < 64.0 &&
     longitude >= 3.0 && longitude < 12.0) {
    ZoneNumber = 32;
  }

  // Special zones for Svalbard
  if(latitude >= 72.0 && latitude < 84.0) {
    if(longitude >= 0.0 && longitude < 9.0)
      ZoneNumber = 31;
    else if(longitude >= 9.0 && longitude < 21.0)
      ZoneNumber = 33;
    else if(longitude >= 21.0 && longitude < 33.0)
      ZoneNumber = 35;
    else if(longitude >= 33.0 && longitude < 42.0)
      ZoneNumber = 37;
  }
  LongOrigin    = static_cast<double>((ZoneNumber - 1) * 6 - 180 + 3); //+3 puts origin in middle of zone
  LongOriginRad = LongOrigin * M_PI / 180.0;

  // compute the UTM Zone from the latitude and longitude
  std::ostringstream oss;
  oss << ZoneNumber << UTMLetterDesignator(latitude);
  utmZone = oss.str();

  eccPrimeSquared = WGS84_ECCSQ / (1.0 - WGS84_ECCSQ);

  N = WGS84_A / sqrt(1.0 - WGS84_ECCSQ * sin(LatRad) * sin(LatRad));
  T = tan(LatRad) * tan(LatRad);
  C = eccPrimeSquared * cos(LatRad) * cos(LatRad);
  A = cos(LatRad) * (LongRad - LongOriginRad);

  M = WGS84_A * ((1.0 - WGS84_ECCSQ / 4.0 - 3.0 * WGS84_ECCSQ * WGS84_ECCSQ / 64.0 - 5.0 * WGS84_ECCSQ * WGS84_ECCSQ * WGS84_ECCSQ / 256.0) * LatRad - (3.0 * WGS84_ECCSQ / 8.0 + 3.0 * WGS84_ECCSQ * WGS84_ECCSQ / 32.0 + 45.0 * WGS84_ECCSQ * WGS84_ECCSQ * WGS84_ECCSQ / 1024.0) * sin(2.0 * LatRad) + (15.0 * WGS84_ECCSQ * WGS84_ECCSQ / 256.0 + 45.0 * WGS84_ECCSQ * WGS84_ECCSQ * WGS84_ECCSQ / 1024.0) * sin(4.0 * LatRad) - (35.0 * WGS84_ECCSQ * WGS84_ECCSQ * WGS84_ECCSQ / 3072.0) * sin(6.0 * LatRad));

  utmEasting = k0 * N * (A + (1.0 - T + C) * A * A * A / 6.0 + (5.0 - 18.0 * T + T * T + 72.0 * C - 58.0 * eccPrimeSquared) * A * A * A * A * A / 120.0) + 500000.0;

  utmNorthing = k0 * (M + N * tan(LatRad) *
                            (A * A / 2.0 +
                             (5.0 - T + 9.0 * C + 4.0 * C * C) * A * A * A * A / 24.0 + (61.0 - 58.0 * T + T * T + 600.0 * C - 330.0 * eccPrimeSquared) * A * A * A * A * A * A / 720.0));
  if(latitude < 0.0) {
    utmNorthing += 10000000.0; //10000000 meter offset for southern hemisphere
  }
}

void UTMtoLL(double utmNorthing, double utmEasting, const std::string& utmZone, double& latitude, double& longitude) {
  // converts UTM coords to lat/long.  Equations from USGS Bulletin 1532
  // East Longitudes are positive, West longitudes are negative.
  // North latitudes are positive, South latitudes are negative
  // Lat and Long are in decimal degrees.
  // Written by Chuck Gantz- chuck.gantz@globalstar.com

  double k0 = 0.9996;
  double eccPrimeSquared;
  double e1 = (1.0 - sqrt(1.0 - WGS84_ECCSQ)) / (1.0 + sqrt(1.0 - WGS84_ECCSQ));
  double N1, T1, C1, R1, D, M;
  double LongOrigin;
  double mu, phi1, phi1Rad;
  double x, y;
  int    ZoneNumber;
  char   ZoneLetter;
  bool   NorthernHemisphere;

  x = utmEasting - 500000.0; //remove 500,000 meter offset for longitude
  y = utmNorthing;

  std::istringstream iss(utmZone);
  iss >> ZoneNumber >> ZoneLetter;
  if((static_cast<int>(ZoneLetter) - static_cast<int>('N')) >= 0) {
    NorthernHemisphere = true; //point is in northern hemisphere
  }
  else {
    NorthernHemisphere = false; //point is in southern hemisphere
    y -= 10000000.0;            //remove 10,000,000 meter offset used for southern hemisphere
  }

  LongOrigin = (ZoneNumber - 1.0) * 6.0 - 180.0 + 3.0; //+3 puts origin in middle of zone

  eccPrimeSquared = WGS84_ECCSQ / (1.0 - WGS84_ECCSQ);

  M  = y / k0;
  mu = M / (WGS84_A * (1.0 - WGS84_ECCSQ / 4.0 - 3.0 * WGS84_ECCSQ * WGS84_ECCSQ / 64.0 - 5.0 * WGS84_ECCSQ * WGS84_ECCSQ * WGS84_ECCSQ / 256.0));

  phi1Rad = mu + (3.0 * e1 / 2.0 - 27.0 * e1 * e1 * e1 / 32.0) * sin(2.0 * mu) + (21.0 * e1 * e1 / 16.0 - 55.0 * e1 * e1 * e1 * e1 / 32.0) * sin(4.0 * mu) + (151.0 * e1 * e1 * e1 / 96.0) * sin(6.0 * mu);
  phi1    = phi1Rad / M_PI * 180.0;

  N1 = WGS84_A / sqrt(1.0 - WGS84_ECCSQ * sin(phi1Rad) * sin(phi1Rad));
  T1 = tan(phi1Rad) * tan(phi1Rad);
  C1 = eccPrimeSquared * cos(phi1Rad) * cos(phi1Rad);
  R1 = WGS84_A * (1.0 - WGS84_ECCSQ) /
       pow(1.0 - WGS84_ECCSQ * sin(phi1Rad) * sin(phi1Rad), 1.5);
  D = x / (N1 * k0);

  latitude = phi1Rad - (N1 * tan(phi1Rad) / R1) * (D * D / 2.0 - (5.0 + 3.0 * T1 + 10.0 * C1 - 4.0 * C1 * C1 - 9.0 * eccPrimeSquared) * D * D * D * D / 24.0 + (61.0 + 90.0 * T1 + 298.0 * C1 + 45.0 * T1 * T1 - 252.0 * eccPrimeSquared - 3.0 * C1 * C1) * D * D * D * D * D * D / 720.0);
  latitude *= 180.0 / M_PI;

  longitude = (D - (1.0 + 2.0 * T1 + C1) * D * D * D / 6.0 + (5.0 - 2.0 * C1 + 28.0 * T1 - 3.0 * C1 * C1 + 8.0 * eccPrimeSquared + 24.0 * T1 * T1) * D * D * D * D * D / 120.0) / cos(phi1Rad);
  longitude = LongOrigin + longitude / M_PI * 180.0;
}
} // namespace camodocal
